I should also note it's debatable whether psychology is reducible to biology. Some parts are. Arguably the parts that they can actually make headway in. But I think some fundamental parts aren't. There's actually still a bit of an ongoing debate as to whether biology is reducible to physics. Although enough people are physicalists so as to have faith that it is.

I think the same argument can be made in each of the steps. To say "physics is just applied mathematics", for example, is to say that you can derive the universe from pure math, which just doesn't work. Not only that, but as an experimentalist, I must say that another good response is that this also arranges field by utility, with the arrow going the opposite direction.